1. Field of the Invention
The invention relates in generally to nonlinear electronic control system optimization.
2. Description of the Related Art
Feedback control systems are widely used to maintain the output of a dynamic system at a desired value in spite of external disturbances that would displace it from the desired value. For example, a household space-heating furnace, controlled by a thermostat, is an example of a feedback control system. The thermostat continuously measures the air temperature inside the house, and when the temperature falls below a desired minimum temperature the thermostat turns the furnace on. When the interior temperature reaches the desired minimum temperature, the thermostat turns the furnace off. The thermostat-furnace system maintains the household temperature at a substantially constant value in spite of external disturbances such as a drop in the outside temperature. Similar types of feedback controls are used in many applications.
A central component in a feedback control system is a controlled object, a machine or a process that can be defined as a “plant”, whose output variable is to be controlled. In the above example, the “plant” is the house, the output variable is the interior air temperature in the house and the disturbance is the flow of heat (dispersion) through the walls of the house. The plant is controlled by a control system. In the above example, the control system is the thermostat in combination with the furnace. The thermostat-furnace system uses simple on-off feedback control system to maintain the temperature of the house. In many control environments, such as motor shaft position or motor speed control systems, simple on-off feedback control is insufficient. More advanced control systems rely on combinations of proportional feedback control, integral feedback control, and derivative feedback control. A feedback control based on a sum of proportional feedback, plus integral feedback, plus derivative feedback, is often referred as a PID control.
A PID control system is a linear control system that is based on a dynamic model of the plant. In classical control systems, a linear dynamic model is obtained in the form of dynamic equations, usually ordinary differential equations. The plant is assumed to be relatively linear, time invariant, and stable. However, many real-world plants are time varying, highly non-linear, and unstable. For example, the dynamic model may contain parameters (e.g., masses, inductance, aerodynamics coefficients, etc.), which are either only approximately known or depend on a changing environment. If the parameter variation is small and the dynamic model is stable, then the PID controller may be satisfactory. However, if the parameter variation is large or if the dynamic model is unstable, then it is common to add adaptive or intelligent (AI) control functions to the PID control system.
AI control systems use an optimizer, typically a non-linear optimizer, to program the operation of the PID controller and thereby improve the overall operation of the control system.
Classical advanced control theory is based on the assumption that near of equilibrium points all controlled “plants” can be approximated as linear systems. Unfortunately, this assumption is rarely true in the real world. Most plants are highly nonlinear, and often do not have simple control algorithms. In order to meet these needs for a nonlinear control, systems have been developed that use soft computing concepts such as genetic algorithms (GA), fuzzy neural networks (FNN), fuzzy controllers and the like. By these techniques, the control system evolves (changes) in time to adapt itself to changes that may occur in the controlled “plant” and/or in the operating environment.
Many controlled plants must be moved from one control state to another control state in a stepwise fashion. For example, a stepping motor moves by stepping in controlled increments and cannot be arbitrarily moved from a first shaft position to a second shaft position without stepping through all shaft positions in between the first shaft position and the second shaft position. Prior art control systems based on soft computing with genetic analyzer are not necessarily well suited for plants that must be changed or controlled in a stepwise fashion, in part because of the operation of the genetic analyzer. The chromosomes of a genetic analyzer are typically coded with the values of one or more control parameters used to control the plant. The genetic optimizer finds new control parameters without regard to the value of the previous control parameters or the constraints imposed by the plant in moving from the previous control parameters to the new control parameters.